The ozonization mechanism for polycyclic aromatic hydrocarbons (PAHs) and soot is investigated by quantum mechanical calculations carried out on molecular and periodic systems. PAHs, interesting per se, serve also to model the local features of the graphenic soot platelets, for which another model is provided by a periodic representation of one graphenic layer. A concerted addition leads to a primary ozonide, while a nonconcerted attack produces a trioxyl diradical (in which one of the two unpaired electrons is pi-delocalized). Easy loss Of (i) O-1(2) or (ii) O-3(2) from either intermediate, with spin conservation, would yield stable (i) singlet or (ii) triplet pi-delocalized species which carry an epoxide group. The trioxyl diradical pathway is estimated to be preferred, in these systems. An intersystem crossing, taking place in the trioxyl diradicals, can be invoked to allow the even easier loss of a ground-state oxygen molecule with the formation of a ground-state epoxide in a more exoergic and less demanding step. We propose that soot ozonization can take place by such a process, with ultimate functionalization of the graphenic platelets by epoxide groups.